International Journal of Energy Engineering 2012, 2(2): 29-35
DOI: 10.5923/j.ijee.20120202.05
Optimal Location of Multi Type FACTS Devices for
Multiple Contingencies Using Genetic Algorithms
Marouani Ismail1,*, Guesmi Tawfik2, Hadj Abdallah Hsen3
1
Electrical engineering Department, High institute of technological studies, Kasserine, 1200, Tunisia
2
Electrical engineering Department, Biomedical institute of Tunisia, Tunisia, 1006, Tunisia
3
Electrical engineering Department, National engineering school of Sfax, Sfax, 3038, Tunisia
Abstract With the electricity market deregulation, the number of unplanned power exchanges increases. If these ex-
changes are not controlled, some lines may become overloaded. Network contingencies often contribute to overloading of
branches, violation of voltages and also leading to problem security. This paper presents a procedure based on the contingency severity index (CSI) described by a real power flow performance index (PI) to place multi type FACTS devices
(Flexible AC Transmission System) in order to eliminate or alleviate the line over loads. TCSC and UPFC are considered
and modeled for steady state analysis. Once the location is determined, their type, their optimal settings and cost of installation can be obtained by solving the optimization problem using genetic algorithms (GA). The proposed approach is tested on
9-bus test system.
Keywords
Performance Index, Contingency Severity Index, FACTS devices, GA
1. Introduction
Concept FACTS (Flexible Alternating Current Transmission Systems) includes all the devices based on power electronics. This concept makes the improving transfert of
power flow possible. The technology of these systems ensures a higher speed than the traditional electromechanical
systems[1].
Both the choice of the adapted FACTS devices and its site
in the electrical supply network, depend on the objectives we
want to reach.
In stationary regime, the FACTS devices are used to control the transits of powers in order to eliminate or reduce the
overloads in the lines and control the voltage at load buses.
The required objectives have either technical nature or
economic one [2,3]. FACTS devises include TCSC (Thyristor Controlled Seies Compensator), SVC (Static Var
Compensator), UPFC (Unified Power Flow Controller), etc.
A method discussed in[4], applied the optimal placement
of a shunt device placed in a long line to increase the capacity
of the transmissible power by improving the stability of
system. Similar methods presented in[5] concerning the
placement of the FACTS to increase the voltage stability,
based on a nodal analysis of the equations of the load flow
modified by the FACTS. A hybrid method based on the
genetic algorithms and the linear programming presented
* Corresponding author:
ismail.marouani@isetks.rnu.tn (Marouani Ismail)
Published online at http://journal.sapub.org/ijee
Copyright © 2012 Scientific & Academic Publishing. All Rights Reserved
in[6] to find optimal placement of multiples SVC. The objectives are first to prevent the voltage collapse and second
minimize the investment cost. The method presented in[7]
determines the optimal sites of devices FACTS shunt by a
singular analysis of the Jacobean matrix. The FACTS are
placed at the nodes having the largest sensitivity of voltage to
the load variations. In the reference[8], the models of
FACTS are integrated in the load flow calculation. They are
used to reduce the real power losses in the network. The
allocation is based on the sensitivity analysis of the losses
expressions to the controllable parameters by FACTS devices.
In this paper, the essential idea of multi type FACTS devices, TCSC and UPFC placement is to determine a branch
which having the most sensitivity for single and double
contingencies. After placing FACTS devices, their Type,
optimal settings and cost of installation can be obtained by
solving the optimization problem. The nonlinear optimization problem is solved by genetic algorithms (GA).
2. FACTS Devices Models
2.1. Transmission Line
The figure.1 shows a simple transmission line represented
by its lumped Π equivalent parameters connected between
bus-i and bus-j. The real and reactive power flow from bus-i
to bus-j can be written as
Pij =
Vi 2 Gij − ViV j [Gij cos(δ ij ) + Bij sin(δ ij )]
(1)
Qij =
−Vi 2 ( B ij + Bsh ) − ViV j [Gij sin(δ ij ) − Bij cos(δ ij )]
(2)
Marouani Ismail et al.: Optimal Location of Multi Type FACTS Devices for
Multiple Contingencies Using Genetic Algorithms
30
Where δ ij= δ i − δ j . Similarly, the real and reactive power
flow from bus-j to bus-i
(3)
Pji =−
V j2 Gij ViV j [cos(δ ij ) − Bij sin(δ ij )]
2
(4)
Q ji =
−V j ( B ij + Bsh ) + ViV j [Gij sin(δ ij ) + Bij cos(δ ij )]
Bus-j
Y=
Gij + jBij
ij
Bus-i
V j ∠δ j
Vi ∠δ i
jBsh
jBsh
2.2. TCSC Model
Figure.2 shows the model of transmission line with TCSC
connected between buses i and j. The TCSC can be considered as a static reactance − jxc . The real and reactive power
flow from bus-i to bus-j, and from bus-j to bus-i of a line
having series impedance and a series reactance are[9]:
(5)
PijTCSC =
Vi 2 Gij' − ViV j [Gij' cos(δ ij ) + Bij' sin(δ ij )]
(6)
QijTCSC =
−Vi 2 ( Bij' + Bsh ) − ViV j [Gij' sin(δ ij ) − Bij' cos(δ ij )]
PjiTCSC =
V j2 Gij' − ViV j [Gij' cos(δ ij ) − Bij' sin(δ ij )]
QTCSC
=
−V j2 ( Bij' + Bsh ) + ViV j [Gij' sin(δ ij ) + Bij' cos(δ ij )]
ji
Where Gij' =
; Bij' =
rij2 + ( xij − xc ) 2
−( xij − xc )
rij2 + ( xij − xc ) 2
(7)
(8)
(10)
QisTCSC = −Vi 2 ∆Bij − ViV j [∆Gij sin δ ij − ∆Bij cos δ ij ]
(11)
= −V ∆Bij + ViV j [∆Gij sin δ ij + ∆Bij cos δ ij ]
(12)
xc rij ( xc − 2 xij )
∆Gij =2
(rij + xij2 )(rij2 + ( xij − xc ) 2 )
and
Q
TCSC
js
2
j
2
j
Where
Bus-j
V j ∠δ j
− jxc
jBsh
B ' *
− Ii )
(15)
2
The active and reactive power flow in the line having
UPFC can be written, with (13)-(15), as
PijUPFC = (Vi 2 + VT2 ) + 2ViVT gij cos(ϕT − δ i )
−V jVT [ gij cos(ϕT − δ j ) + bij sin(ϕT − δ j )]
UPFC
ji
P
= V j2 gij − V jVT [ gij cos(ϕT − δ j ) − bij sin(ϕT − δ j )]
−ViV j ( gij cos δ ij − bij sin δ ij )
QijUPFC =
−Vi I q − Vi 2 [bij +
B
) + ViVT [( gij sin(ϕT − δ j )]
2
B
+(bij + ) cos(ϕT − δ i )] − ViV j ( gij sin δ ij − bij cos δ ij )
2
B
) + V jVT [ gij sin(ϕT − δ j ) + bij cos(ϕT − δ j )]
2
+ViV j ( gij sin δ ij + bij cos δ ij )
QUPFC
=
−V j2 (bij +
ji
jBsh
TCSC
Sis
Figure 3. Injection Model of TCSC
(19)
(20)
B
) cos(ϕT − δ i )]
2
(22)
=
−V jVT [ gij sin(ϕT − δ j ) + bij cos(ϕT − δ j )]
QUPFC
js
(23)
QisUPFC = Vi I q + ViVT [ gij sin(ϕT − δ i ) + (bij +
VT
Vi ∠δ i
I’i
IT
V’i
j
S TCSC
js
(18)
(21)
Iq
Bus-j
(17)
=
PjsUPFC V jVT [ gij cos(ϕT − δ j ) − bij sin(ϕT − δ j )]
Bus-i
Ii
Figure 2. Model of TCSC
rij + jxij
(16)
From basic circuit theory, the injected equivalent circuit of
figure.5 can be obtained. The injected active and reactive
power at bus-i and bus-j and reactive powers of a line having
a UPFC are:
UPFC
Bus-i
(14)
S ji =Pji + jQ ji =
V j I *ji =
V j ( jV j
+bij sin(ϕT − δ j )]
Zij= rij + jxij
Vi ∠δ i
B
+ IT + I q + I i' )*
2
PisUPFC =
−VT2 gij − 2ViVT gij cos(ϕT − δ i ) + V jVT [ gij cos(ϕT − δ j )
− x (r 2 − x 2 + xc xij )
∆Bij =2 c 2 ij 2 ij
(rij + xij )(rij + ( xij − xc ) 2 )
Bus-i
Sij = Pij + jQij = Vi I ij* = Vi ( jVi
−ViV j ( gij cos δ ij + bij sin δ ij )
= V ∆Gij − ViV j [∆Gij cos δ ij − ∆Bij sin δ ij ]
P
π
2
Re[VT I i'* ]
(13)
Arg ( IT ) = Arg (Vi ) , IT =
Vi
The power flow equations from bus-i to bus-j and from
bus-j to bus-I can be written as
.
The change in the line flow due to series capacitance can
be represented as a line without series capacitance with
power injected at the receiving and sending ends of the line
as shown in Figure.3. The real and reactive power injections
at bus-i and bus-j can be expressed as
(9)
PisTCSC= Vi 2 ∆Gij − ViV j [∆Gij cos δ ij + ∆Bij sin δ ij ]
TCSC
js
The model of UPFC placed in lin-k connected between
bus-i and bus-j is shown in figure.4. UPFC has three controllable parameters, namely, the magnitude and the angle of
inserted voltage (VT, ϕT ) and the magnitude of the current
(Iq).
Based on the equivalent circuit of UPFC and the vectorial
diagram (Figure.4), the basic mathematical relations can be
given as
=
( I q ) Arg (Vi ) ±
Vi=' Vi + VT , Arg
Figure 1. Transmission line mode
rij
2.3. UPFC Model
B
2
(a)
rij + jxij
Bus-j
V j ∠δ j
j
B
2
International Journal of Energy Engineering 2012, 2(2): 29-35
31
The real power flow PI sensitivity factors with respect to
the control parameters of UPFC and TCSC can be defined as
Vi '
Iq
VT
Vi
Ii
ϕT
Vj
Bus-j
Y=
ij gij + jbij
UPFC
Sis
Figure 5.
, β = ∂PI
k
VT ∂ϕT
VT = 0
γk =
ϕT = 0
∂PI
∂xc
xc = 0
Using (24), the sensitivity of PI with respect to FACTS
(UPFC, TCSC) parameter Xk ( VT , ϕT and xc ) connected between bus-i and bus-j can be written as
(25)
Using dc power flow equations[10] where s is slack bus,
the real power flow in a branch-m ( Plm ) can be represented by
Schematic diagram of UPFC, Equivalent circuit (a), Vector
diagram (b)
Bus-i
∂PI
∂VT
∂P
∂PI
1
N
= ∑ mb=1 ωm Plm3 ( max ) 4 lm
∂X k
∂X k
Plm
(b)
Figure 4.
αk =
S UPFC
js
Injection model of UPFC
3. Problem Formulation
3.1. Placement of FACTS Devices
The essential idea of the proposed multi type FACTS devices, UPFC and TCSC placement approaches is to determine a branch which has more sensibility for the large list of
single and double contingencies which are defined as the
following:

Single Contingency is aimed at eliminating successively all the branches and transformers of the network
element by element. For each elimination we make an
analysis of security constraints. When an overload in the
lines or there is a variation of the levels of the critical voltage
appears. We look for the optimal configurations of FACTS
devices for which the network turns to its normal situation.

Double contingency is aimed at eliminating two
elements simultaneously, keeping the same operations done
with single contingency.
This section will describe the definition and calculation of
the contingency severity index and the optimal placement
procedure for the UPFC and TCSC.
3.1.1. Performance Index: PI
The severity of the system loading under normal and
contingency cases can be described by a real power line flow
performance index[10], as given in the following:
Plm 2 n
N ω
(24)
)
PI = ∑ m =1 m ( max
b
2n Plm
Where Plm is the real power flow and Plmmax is the rated capacity of the branch-m, ωm a real nonnegative weighting
coefficient of the branches and n is the exponent. N b is the
total number of branches in the network.
In this paper the value of the exponent has been taken as 2
and ωi = 1 . It was found that the masking effect was removed
with this value for the considered examples[11].
∑ nN=B1 Smn Pn
for m ≠ k
 n≠ s
Plm =  N
B
k
∑ n =1 Smn Pn + Pjs for m =
 n≠ s
(26)
Where Smn is the mnth element of matrix [S] that relates
line flow with power injections at the buses without FACTS,
NB is the number of buses in the system.
Using (25) and (26), the following relations can be derived
 ∂PisFACTS
∂PjsFACTS
) for m ≠ k
+ Smj
( Smi
∂X k
∂X k
∂Plm 
(27)
=
∂X k  ∂PisFACTS
∂PjsFACTS ∂Pjs
k
( Smi ∂X + Smj ∂X ) + ∂X for m =
k
k
k

3.1.2. Contingency Severity Index :CSI
The CSI for branch “m” is defined as the most valuable
of the sum of the sensitivities of branch “m” taking into
consideration single and multiple contingency, and is expressed as
c
c
c
CSI m = max(∑ α kp ; ∑ β kp ; ∑ γ kp )
(28)
p 1=
p 1=
p 1
=
Where c is the number of contingencies
CSI values are calculated for every branch by using (28).
The branch with the largest CSI is considered as the best
location for Facts devices.
3.2. Optimal Setting of FACTS Devices
The UPFC can be considered as combination of a TCSC in
series with the branch and SVC connected across the corresponding buses between which the branch is connected.
After fixing the location, to determine the best possible
setting of FACTS devices for all possible single and multiple
contingencies, the optimization problem will have to be
solved using GA approach.
The objective function for this work is,
Obj=minimize {SOL and IC}
Ns
SOL = ∑
N
Pk
∑a (P
c 1=
k 1
=
k
k
max
)4
Where:
N: Number of lines.
Ns: Number of single contingency considered.
ak : Weight factor =1.
Pk : Real power transfer on branch k.
(29)
Marouani Ismail et al.: Optimal Location of Multi Type FACTS Devices for
Multiple Contingencies Using Genetic Algorithms
32
: Maximum real power transfer on branch k.
SOL: represents the severity of overloading.
IC: Installation cost of FACTS devices.
Installation cost includes the sum of installation cost of all
the devices and it can be calculated by:
(30)
CTCSC
= 0.0015S 2 − 0.71S + 153.75(US $ / KVAR )
2
(31)
CUPFC = 0.0003S − 0.2691S + 188.22(US $ / KVAR)
Where, S is the operating range of FACTS in MVAR
=
S Q2 − Q1
Pk max
Q1: MVAR flow through the branch before placing
FACTS devices.
Q2: MVAR flow through the branch after placing FACTS
devices
The objective function is solved with the following constraints:
3.2.1. Security Limits
Two inequality constraints are considered. The first constraint includes voltage limits at load buses as shown in (32)
min ≤ V ≤ V max , i = 1, ,..., N
(32)
VLi
Li
L
Li
Where
max
Vmin and VLi
Li
are respectively lower and upper
limits voltage at load buses.
The second is represented by the line flow limits. It considers that the real power flow Pli in each transmission
line i among the Nline lines of the power system must be
lower than its maximum value
be written as :
Pmax .
li
Mathematically, it can
max i = 1,..., N
Pli ≤ Pli
line
Where
∑ P : Total power generation.
∑ : Total power demand.
PL : Losses in the transmission network.
G
PD
4. Overview of GA
In this paper, GA has been used for choice and setting
parameters of the FACTS devices. The first step GA is to fix
a random initial population, which is a set of candidate solutions. In general, candidate solutions are represented as
coded number corresponding to each variable of the optimization problem, called chromosome. Also, for each individual, a fitness function, related to the objective function, is
affected. GA operates in generations.
One generation is as follows :
● For each individual of the current population, a fitness
function is affected.
● One or more parents are chosen according to their fitness function.
● GA operators, such as, crossover and mutation are applied to parents to produce children.
● Theses children are inserted into the following population.
This process is repeated until the population size is
reached.
gen=1
Fix the GA parameters
(33)
Generate randomly initial population
3.2.2. Voltage Stability Constraint
VS includes voltage stability constraints in the objective
function and is given by:
0

VS =
0.95 − Vb
Vb − 1.05

if
if
if
0.9 < Vb < 1.1
Vb < 0.9
Vb > 1.1
(34)
Where, Vb: voltage at bus b.
Calculate the fitness of each individual
Calculate the fitness of each individual in
the current population
Apply GA operators
(selection, crossover and mutation)
3.2.3. FACTS Devices Constraints:
The FACTS devices limit is given by:
−0.5 X L < xc < 0.5 X L
− 200 MVAR ≤ QUPFC ≤ 200 MVAR
(35)
(36)
Where:
XL: Original line reactance in (pu).
xc: Reactance added to the line where TCSC is placed in
(pu)
QUPFC: reactance power injected at UPFC placed in
MVAR.
Calculate the fitness of each individual
in the current population
gen=gen+1
No
Gen>max_gen
3.2.4. Power Balance Constraints
Yes
The power balance equations are given by:
∑
=
PG
∑
PD + PL
(37)
Stop
Fgure 6. Flow chart of the GA
International Journal of Energy Engineering 2012, 2(2): 29-35
The flow chart of the GA can be as in the following figure.
The optimal configuration of the FACTS devices is encoded by its location and control parameters.
The location is defined by the number Nb of branch where
it is installed and the number N B of the bus where the parallel component of UPFC is connected. VT , ϕT , and xc are
considered as the control parameters.
The proposed GA has been implemented using real-coded
genetic algorithm[12]. So, a chromosome X corresponding
to a decision variable is represented as a string of real values
xi , i.e. X = x1x2 ...xlchrom . lchrom is the chromosome
size and xi is a real number within its lower limit ai and
upper limit bi . i.e. xi ∈ ai , bi  . Thus, for two individuals
having as chromosomes respectively X and Y and after
generating a random number α ∈ [0,1] , the crossover operator can provide two chromosomes X' and Y' with a
probability PC as follows:
X' = αX + ( 1 - α ) Y

Y' = ( 1 - α ) X + αY
chromosome X will be transformed to other parameter x'i
with a probability Pm as follows :
(
(
)
)

xi + Δ t, bi - xi , if τ = 0
x'i = 

xi - Δ t, xi - ai , if τ = 1

Δ ( t, y ) = y  1 - ε
β
( 1-t/gmax ) 
5.2. Double Contingency
Considering two branches outaged at a time for 6 branches,
15 doubles contingency combinations are available. Considering all the double contingency combinations, the 6
branches are ranked based on their CSI values, are given in
table 1.
Table 1 shows that, branch number 2-3, 1-2 is chosen as
the best location to place the first available multi type
FACTS devices for single and double contingencies. The
placement of other FACTS devices can proceed where
branch 1-2, 1-6 will be the second choice, depending on the
available budget. Branch 1-6, 2-3 are the third choice and so
on. Once the location is determined, their optimal setting,
their type and cost of installation can be obtained by solving
the optimization problem using GA.
The table 2 shows the overloading of branches when different numbers of FACTS devices are installed.
Table 1. Ranking of branches for 9-bus test system
(38)
In this study, the non-uniform mutation operator has been
employed. So, at the tth generation, a parameter xi of the
33
1. Simple contingence
Rang
1
2
3
4
5
6
Branch
2-3
1-2
1-6
3-5
4-5
4-6
CSI
0.0421
0.0362
0.0329
0.0278
0.0256
0.0213
2. Double contingence
Rang
1
2
3
4
5
6
Branch
1-2
1-6
2-3
4-5
4-6
3-5
CSI
0.7911
0.7059
0.5381
0.3823
0.3117
0.2855
(39)
Table 2. 1. Simple contingence
(40)




Where τ is random binary number, r is a random
number ε ∈ [0,1] and g max is the maximum number of
generations. β is a positive constant chosen arbitrarily.
In this work the fitness is defined as follows:
(41)
Fitness function= SOL + (λ1 *VS ) + (λ2 * IC )
Where :
λ1 : Penalty factor
λ2 : Scaling factor
5. Simulation Results
The solution for optimal location of FACTS devices to
minimize the installation cost of FACTS devices and overloads for 9-bus WSCC (Western System Coordinating
Council) test system were obtained in this section. Both the
bus data and line data of the 9-bus test system are taken
from[13].
5.1. Single Contingency
The location of FACTS devices depends upon the CSI
values which are calculated for 6 branches by considering all
single contingencies. Then the branches are ranked according to their values of CSI which are given in table 1.
No. of
devices
SOL
No.of
overloads
FACTS devices
cost(US$)
Fitness Function
0
52.2512
17
0
0
1
40.9669
13
1.6706e+006
2.4315 e+008
2
37.2156
12
3.5003e+006
1.9562e+008
3
30.5820
09
3.3970e+006
1.6925e+008
4
33.0019
11
4.1231e+006
1.7439e+008
2. Double contingence
No. of
devices
SOL
No.of overloads
FACTS devices
cost(US$)
Fitness
Function
0
113.09
21
0
0
1
108.57
16
1.5217e+006
4.1837e+008
2
97.23
12
3.0129e+006
3.5618e+008
3
102.41
15
4.1833e+006
3.6317e+008
4
111.07
17
6.8813e+006
5.6331e+008
Table 2 shows the reduction of the severity index (SOL)
and the number of the overloads from 17 to 09 when three
FACTS devices are installed for simple contingencies, and
from 21 to 12 when two FACTS devices for double contingencies. From this situation, if there is an increase in a
number of FACTS devices, SOL and cost of installation start
to increase also. Hence in this case, the number 3 and 2 are
Marouani Ismail et al.: Optimal Location of Multi Type FACTS Devices for
Multiple Contingencies Using Genetic Algorithms
considerable for the optimal system security of the network
for simple and double contingencies. The optimal arrangements, the corresponding line and the type of FACTS devices are obtained in table 3 by solving the optimization
problem using GA.
Table 3. Optimal setting multi type FACTS devices
1. Simple contingence
No. of
devices
Branch
number
1
2-3
Type of device
TCSC
UPFC
0
1
2-3
1-6
1-2
2-3
1-6
1-2
2-3
1-6
4-5
2
3
4
0
2
1
2
0
4
Reactance
xc (pu)
Reactive
power
QSVC
(MVAR)
0.5173
-87.1815
0.3719
0.4127
0.1791
0.3857
0.2231
-0.2758
0.1308
-0.6314
0.5051
-66.9217
-37.8580
0
-92.3917
-57.2110
-88.1934
-71.3215
-52.4361
-67.5805
2. Double contingence
UPFC
Reactance
xc (pu)
Reactive
power
QSVC
(MVAR)
1
0
0.5173
0
1
1
0
3
0
4
Type of device
No. of
devices
Branch
number
TCSC
1
2-3
1-6
2-3
2-3
1-6
4-5
1-6
2-3
4-5
1-2
2
3
4
0.3719
0.4127
0.1791
0.3857
0.2231
-0.2758
0.1308
-0.6314
0.5051
+48.19370
-91.2713
20.1170
-77.1495
-81.1850
-53.5319
-37.6817
-89.2051
8
2.5
x 10
4 FACTS Devices
2.4
3 FACTS Devices
Fitness Function
2.3
2.2
2.1
8
4.2
x 10
3 FACTS Devces
2 FACTS Devices
4.1
4
Fitness Function
34
3.9
3.8
3.7
3.6
3.5
0
20
40
60
80
100
120
140
Number of Population
160
180
200
Figure 8. Fitness convergence curve for double contingency
Table 4.
GA parameters
Number of generations
200
Population size
100
Crossover probability
0.85
Mutation probability
0.02
Type of selection
Tournament
5.3. Effects of FACTS Devices
In order to verify the presented models of FACTS devices,
the effectiveness of the approach proposed and illustrate the
impacts of FACTS devices on power losses in transmission
lines and voltage deviation at load buses, we study three
cases for a test system 9-bus.
Case 1: results without FACTS.
Case 2: results with FACTS devices for simple contingencies, for the optimal system security of the network.
Case 3: results with FACTS devices for double contingencies, for the optimal system security of the network.
The voltage profile at load buses of the system with and
without the FACTS devices are shown in Fig.9. As shown in
the figure, the voltage at all buses is in the acceptable limits
(0.9<Vi<1.1 pu) and improved significantly with the FACTS
devices installed for the optimal system security of the network system .
2
1.9
1.8
1.7
1.6
0
20
40
60
80
100
120
140
Number of Population
160
180
200
Figure 7. Fitness convergence curve for single contingency
Figure.7 and figure.8 represent the fitness convergence
curve for single and double contingencies. The simulation
carried out with multiple runs to get the optimal results of
multi type FACTS devices. GA parameters used in this work
are taken in table 4.
Figure 9. Voltage profile after and before employing FACTS devices
Figure.10 shows the effects of FACTS devices on active
and reactive power losses in the transmission lines of the
system, where they are installed for the optimal system se-
International Journal of Energy Engineering 2012, 2(2): 29-35
curity of the network, for simple and double contingencies.
[1]
G. S. Eskandar, "Apport de l'UPFC à l'amélioration de la
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0.05
Active power losses
0.04
0.03
0.02
Reactive power
losses
0.01
0
Case 1
Case 2
Case 3
Figure 10. Evolution of the active and reactive power losses with and
without FACTS
6. Conclusions
In this paper, a sensitivity-based approach has been used
to find (for finding) suitable placement of FACTS devices
along the system branches based on the CSI values to alleviate system overloads and to improve the system security
margin, considering simple and double contingencies. The
type of device to be placed. cost of installation and their
settings were taken as the optimization parameters for both
single and double contingencies. This optimization problem
is solved using GA techniques. TCSC and UPFC are considered in this work. It is observed that the system security
margin can not be improved further after placing some optimal number of multi type FACTS devices. 9-bus test system is used to evaluate the performance of these approaches.
Appendix
The 9-bus western system coordinating council (WSCC)
system is shown on one-line diagram. The system contains
three generators at buses 9, 8 and 7. Bus 9 is considered as
the slack bus. All data of the system are marked in the
one-line
diagram of the system . Theses values are given in pu.
Considering a base power of 100 MVA for the overall system and base voltages of 16.5 kv for bus 9, 18.1 kv for bus 8,
13.8 kv for bus 7, and 230 kv for all other buses.
35
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